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IEICE Transactions on Communications

An Efficient Weighted Bit-Flipping Algorithm for Decoding LDPC Codes Based on Log-Likelihood Ratio of Bit Error Probability

Tso-Cho Chen, Erl‐Huei Lu, Chia-Jung LI, Kuo-Tsang Huang

Published Jan 1, 2017• 1 citation
Publisher

Abstract

In this paper, a weighted multiple bit flipping (WMBF) algorithman for decoding low-density parity-check (LDPC) codes is proposed first. Then the improved WMBF algorithm which we call the efficient weighted bit-flipping (EWBF) algorithm is developed. The EWBF algorithm can dynamically choose either multiple bit-flipping or single bit-flipping in each iteration according to the log-likelihood ratio of the error probability of the received bits. Thus, it can efficiently increase the convergence speed of decoding and prevent the decoding process from falling into loop traps. Compared with the parallel weighted bit-flipping (PWBF) algorithm, the EWBF algorithm can achieve significantly lower computational complexity without performance degradation when the Euclidean geometry (EG)-LDPC codes are decoded. Furthermore, the flipping criterion does not require any parameter adjustment.

DOI
10.1587/transcom.2016ebp3376

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In this paper, a weighted multiple bit flipping (WMBF) algorithman for decoding low-density parity-check (LDPC) codes is proposed first. Then the improved WMBF algorithm which we call the efficient weighted bit-flipping (EWBF) algorithm is developed. The EWBF algorithm can dynamically choose either multiple bit-flipping or single bit-flipping in each iteration according to the log-likelihood ratio of the error probability of the received bits. Thus, it can efficiently increase the convergence speed of decoding and prevent the decoding process from falling into loop traps. Compared with the parallel weighted bit-flipping (PWBF) algorithm, the EWBF algorithm can achieve significantly lower computational complexity without performance degradation when the Euclidean geometry (EG)-LDPC codes are decoded. Furthermore, the flipping criterion does not require any parameter adjustment.
In this paper a fast version of the parallel weighted bit flipping LDPC decoding algorithm (PWBF) is presented. The idea, which allowed decreasing the computational complexity of the PWBF method, is based on the observation that in dependency on signal to noise ratio, many of the received bits in the codeword of LDPC code could be without error. The augmented algorithm makes tests based on syndromes and symbol involvement in parity checks, which are given by the factor graph corresponding to the chosen LDPC code in order to define so called guaranteed bits. These guaranteed bits do not participate in the decoding calculations further. Simulation results are presented, which show that there is not visible any significant performance deterioration by application of this method and that the approximate speed up of the decoding for the tested codes is about 25% on the selected hardware in comparison with the known PWBF.
Aiming at seeking a low-complexity decoder with fast decoding convergence speed for short or medium low-density parity-check (LDPC) codes, an improved parallel weighted bit-flipping (IPWBF) algorithm, which is applied flexibly for two classes of codes is presented here. For LDPC codes with low column weight in their parity check matrix, both bootstrapping and loop detection procedures, described in the existing literature, are included in IPWBF. Furthermore, a novel delay-handling procedure is introduced to prevent the codeword bits of high reliability from being flipped too hastily. For large column weight finite geometry LDPC codes, only the delay-handling procedure is included in IPWBF to show its effectiveness. Extensive simulation results demonstrate that the proposed algorithm achieves a good tradeoff between performance and complexity.
An adaptive weighted multibit-flipping (AWMBF) decoding algorithm which flips multiple bits in each iteration is proposed for low-density parity-check (LDPC) codes. The multibit-flipping criterion is devised based on the least reliable positions in which reliability measure threshold is dynamically adapted during the decoding process. The proposed decoder converges faster and provides better performances than the conventional weighted bit-flipping and multibit-flipping decoders. Simulation results demonstrate that the proposed algorithm achieves a good tradeoff between performance and complexity.
The reliability ratio weighted based bit-flipping (RRWBF) algorithm for decoding low-density parity-check (LDPC) codes has recently been developed to provide the best performance among all existing bit-flipping based algorithms. The implementation efficient reliability ratio weighted based bit-flipping (IERRWBF) algorithm speedup the original algorithm to decrease the processing time used. A drawback for this algorithm is the decrease in the improvement as the maximum number of iterations assigned for the algorithm increase as a large percentage of decoding time is spent on the iteration part without any change in the performance. In this paper, a modified version for this algorithm is proposed to solve this drawback by reducing the number of iterations required to achieve the same performance of the existing IERRWBF algorithm using efficient number of iterations instead of using the maximum number of iterations for decoding without any change in the performance of the IERRWBF.
To reduce loop-oscillation errors occurring in the weighted bit-flipping algorithm,a hybrid weighted bit-flipping decoding algorithm for low-density parity-check(LDPC) codes is proposed.The proposed algorithm updates multiple bits in each iteration,a random perturbation is added when the loop oscillation is detected which could reduce loop-oscillation errors by changing objective function.And these errors are analyzed from the mathematic perspective.Simulation results and complexity comparison show that the proposed algorithm achieves an appealing tradeoff among performance,convergence and complexity for structured LDPC codes compared with the best known weighted bit-flipping decoding algorithm.